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 A218476 Number of 3n-length 6-ary words, either empty or beginning with the first letter of the alphabet, that can be built by repeatedly inserting triples of identical letters into the initially empty word. 2
 1, 1, 16, 331, 7746, 195011, 5153626, 140995716, 3958980906, 113434797571, 3303283462836, 97478710394451, 2908594804576416, 87605427983818356, 2659959016770389896, 81330226479826092536, 2501989790308939894026, 77386492111973937031491, 2405093253522796180052056 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) = 1/n * Sum_{j=0..n-1} C(3*n,j)*(n-j)*5^j for n>0, a(0) = 1. Recurrence: 2*n*(2*n-1)*(9*n-11)*a(n) = 3*(2997*n^3 - 5769*n^2 + 2754*n - 200)*a(n-1) - 3240*(3*n-5)*(3*n-4)*(9*n-2)*a(n-2). - Vaclav Kotesovec, Aug 31 2014 a(n) ~ 3^(3*n-7/2) * 5^(n+1) / (sqrt(Pi) * n^(3/2) * 4^n). - Vaclav Kotesovec, Aug 31 2014 MAPLE a:= n-> `if`(n=0, 1, add(binomial(3*n, j)*(n-j)*5^j, j=0..n-1)/n): seq(a(n), n=0..20); CROSSREFS Column k=6 of A213027. Sequence in context: A246876 A176128 A223394 * A240344 A068368 A013993 Adjacent sequences:  A218473 A218474 A218475 * A218477 A218478 A218479 KEYWORD nonn AUTHOR Alois P. Heinz, Oct 29 2012 STATUS approved

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Last modified October 17 04:02 EDT 2019. Contains 328106 sequences. (Running on oeis4.)